@sonsx7
I think you will have problems.
We have the battery camera, which is part of the floodlight fixture. Ours is plugged in with the optional power cable, so it is "Live" and online all the time. The camera in the floodlight fixture is designed to be plugged into the fixture, with power at all times, so it would function as ours does.
If the camera is connected to power part of the time and disconnected part of the time, I don't know whether the camera will function as "plugged in" and in "Live" mode at the times when it is connected to power, or whether it will still run on battery power.
In addition, the floodlight portion of the fixture is designed to be controlled from within the Google Home app. It doesn't seem to have a setting for having the lights on all the time. So if you put the floodlight fixture on a timer, I don't think the floodlight will turn on when your timer turns the power on; I think you might have to turn it on within the Google Home app (and I'm not sure you can even do that). And there's no setting to put the floodlight portion itself on a timer; all you can do is specify how long the floodlight should stay on after detecting motion (between 10 seconds and 5 minutes):
https://support.google.com/googlenest/answer/10500343
